They're so different that I'm surprised it's even a question. If anything the illusion of mind is bending them to fit a narrative.
When Relativity explained the precession of Mercury's perihelion the existing physics was off by 1/12,000,000th of Mercury's orbit (per orbit.) Not only was the Ptolemic system off by entire degrees (as opposed to arcseconds which are 1/3,600th of a degree) it was highly dependent on the position of the observer, if you stood on Jupiter I imagine the Ptolemic system would give you complete nonsense as to where the planets would be.
More importantly Newton's work has never been thrown out and you can derive classical mechanics as a special case of Relativity. You can also derive it from quantum mechanics. I don't believe you can show that the geocentric model of the solar system is a special case of the heliocentric model.